The joint spectrum of a tuple of projections
The joint spectrum of a tuple of projections
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投影元组的联合谱
DOI：
10.1360/n012019-00100
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发表时间：
2020-07
影响因子：
--
通讯作者：
Qian Wenhua
中科院分区：
文献类型：
--
作者：
Wu Wenming;Jiang Yecong;Ruan Yingbin;Qian Wenhua
摘要：我们研究了Hilbert空间中投影的联合谱，并计算了一对投影的联合谱。特别地，通过计算I是单位元，P，Q是正则投影对的元组[I，P，Q]的联合谱，我们分别得到了P+Q和PfiQ的谱的特殊刻画。反之，我们证明了C的两个特殊形式的闭子集分别是正则投影对的和与差的谱。我们还计算了满足特定fic条件的投影[P，Q，R]的三元组的联合谱。
Summary: We study the joint spectrum of projections in a Hilbert space, and calculate the joint spectrum of a pair of projections. In particular, by calculating the joint spectrum for a tuple [ I, P, Q ] in which I is the identity and P, Q are a regular pair of projections, we get specific characterizations of the spectra of P + Q and P − Q , respectively. Conversely, we prove that two closed subsets of C in particular forms are respectively the spectra of the sum and the difference of a regular pair of projections. We also calculate the joint spectrum of a 3-tuple of projections [ P, Q, R ] for P, Q and R satisfying some specific conditions.